A health food store sells trail mix made with granola and dried fruit. The store buys granola at $1.00/lb and dried fruit at $2.00/lb, and it sells these items at 25% markup. If the trail mix sells for $1.75/lb, what is the recipe for trail mix?

1 Answer
Aug 9, 2015

Answer:

#("ganola")/("dried fruit") = 3/2#

Explanation:

Suppose a batch of trail mix is made with
#color(white)("XXXX")##g# lb of granola and
#color(white)("XXXX")##f# lb of dried fruit
Then the cost to make a batch would be
#color(white)("XXXX")##1*g + 2*f = g+2f#

With a markup of #25%# the selling price would be
#color(white)("XXXX")##125%# or #5/4# of the cost.

A batch weights
#color(white)("XXXX")##g+f# lb

and at #($1.75)/("lb")#

would sell for a total of #(1.75) * (g+f)#
or #7/4 * (g+f)# dollars.

So
#color(white)("XXXX")##5/4*(g+2f) = 7/4(g+f)#

#rArr##color(white)("XXXX")##5g + 10f = 7g+7f#

#rArr##color(white)("XXXX")##3f = 2g#

That is the ratio of dried fruit to granola is #2:3#